Richard K. Gordon

Complex problem domain based local Petrov-Galerkin meshless method for electromagnetic problems

In this paper, an improved MLPG method has been introduced to simplify the algorithm and thus make it more suitable for dealing with engineering problems with complex domains. In the case of a complex domain with an irregular global boundary, it can be very hard to determine the intersections between the local sub-domains and the global boundary. The improvements of the MLPG method make the MLPG method only require the domain integrations. The intersections between local sub-domains and the global boundary as well as boundary integrations have been avoided. A rectangular problem domain and a circular problem domain with exact solutions have been studied in this paper to investigate the accuracy of the improved MLPG method. The results show that compared to the regular MLPG method, the improved MLPG method can have the same accuracy, but the improved method is much easier to deal with irregular boundaries or complex problem domains.

Using elliptical basis functions in a meshless method to determine electromagnetic fields near material interfaces

In this paper, in addition to employing RBFs in conjunction with a meshless algorithm, an investigation of using elliptical basis functions (EBF) in solving electromagnetics problems in two dimensional regions in which material interfaces are present will be discussed. Numerical results as well as comparisons with analytical solutions will be presented. The effects of the use of these EBFs on the solution accuracy will also be demonstrated.

Electromagnetic Scattering from Impedance Elliptic Cylinders Using Finite Difference Method (Oblique Incidence)

ABSTRACT The electromagnetic scattering from elliptic impedance cylinders illuminated by an obliquely incident plane wave is presented. The finite difference technique is used to solve this problem. Impedance Boundary Condition (IBC) is enforced on the cylinder surface and an Absorbing Boundary Condition (ABC) is applied on the outer boundary. Between the cylinder surface boundary and the outer boundary, the wave equation is solved with the finite difference technique to obtain the scattered field. Two methods are used to solve this problem and comparison between both methods is used to verify the solution. One method is based on transforming the elliptic cylinder into circular cylinder in polar coordinates. The other method is the direct implementation of the finite difference method in the elliptic coordinates. Consequently, proper transformation of IBC, ABC and wave equation is used. The solution obtained from both methods are found to be in good agreement with each other.

High-Level programming of graphics hardware to increase performance of electromagnetics simulation

Modern graphics processing units (GPUs) utilize a programmable parallel pipeline architecture to render complex scenes onto a two-dimensional screen. Rendering these scenes requires rasterization, texturing operations, and multiple stages of lighting operations. These processes are computationally intensive and must be performed near real-time in todays gaming and workstation applications. These industries have driven the performance of GPUs to exceed that of CPUs in terms of operations per second. Much effort has been placed recently on harnessing the power of the GPU for general purpose computation. In this paper, Accelerator by Microsoft Research provides an interface to the GPU using a library of classes and functions in Microsoft C Sharp (C#). The performance of a GPU is compared to a traditional CPU routine in solving matrices generated by a finite element program.

Electromagnetic scattering from conducting bodies of revolution coated with thin magnetic materials

Coating of the conducting objects with thin layers of magnetic materials is used to reduce, significantly, the back scattering from axi-symmetric objects. The concept of the impedance boundary condition (IBC) is used to solve the problem. The present formulation predicts an accurate value of surface impedance from the equivalent volume magnetic current of the magnetic material layer. The IBC concept is used to predict the coating material permeability and thickness in order to reduce the backscattering radar cross section (RCS). The numerical solution is verified by comparison with numerical solutions based on the exact boundary conditions. >

Investigation of the use of a novel meshless technique in the determination of electromagnetic fields in two-dimensional regions

Summary form only given. In recent years there has been a significant amount of research on the use of radial basis functions (RBFs). These functions have very good interpolation qualities, and their use has been primarily in inverse methods. For example, in electromagnetics research, the focus has been primarily on the use of RBFs in the solution of inverse scattering problems. On the other hand, RBFs have not been widely used in partial differential equation (PDE) techniques except in the context of meshless algorithms employing RBFs. While a number of the resulting algorithms have been highly accurate in determining the fields in homogeneous regions, many have also required the use of fully populated matrices that are quite ill-conditioned. In this paper, the use of a novel meshless method inspired by F.A. Fernandez and L. Kulas (Proceedings MIKON-2004, pp. 585-588, 2004) is investigated. Unlike the meshless methods employing RBFs, this method results in a sparsely populated matrix. In general, this matrix has a much lower condition number than does the corresponding matrix resulting from the use of a meshless method employing RBFs. Another advantage of this technique is that when it is used, the field components themselves are the unknowns in the matrix equation under consideration. Thus, the field components are determined directly in the process of solving the matrix equation. On the other hand, in the meshless methods employing RBFs, the unknowns are the coefficients of the RBFs. After these are determined, the additional step of computing the field components from the RBFs and their coefficients is required. In this paper, the formulation of this new method will be discussed in detail and numerical results for several cases will be presented. Comparisons with results obtained using RBFs will be presented and discussed. The condition numbers of the matrices resulting from the two different approaches will also be presented and discussed.

On the Investigation of Phase Error of Cubic Wavelet-Like Functions in a Finite Element Time Domain Algorithm

In this research, the phase error associated with using cubic wavelet-like functions in a finite element time domain solution of Maxwells equations in two dimensions is investigated. A brief discussion of the generation of the cubic wavelet-like functions is presented. Several example problems will be presented in which some of the advantages and disadvantages of the algorithm will be discussed. In these examples, solutions obtained with the finite element time domain algorithm utilizing cubic wavelet-like functions, analytic solutions, and solutions obtained by the traditional finite difference time domain method will be compared.